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Old 08-17-2005, 08:32 PM
Izverg04 Izverg04 is offline
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Join Date: Mar 2004
Posts: 55
Default Re: Apples vs. Oranges

[ QUOTE ]
Game A (Sample size 1175 events)

$/event $0.95
SD$/event $17.90
Bankroll required for .5% ROR = $1388
Multitable earn = $23.69/hr

Game B (Sample size = 930 events)
$/event = $6.83
SD$/event = $83.41
Bankroll required for 0.5% ROR = $2699.18
Multitable earn = $24.24/hr


Both of these allow me to make my weekly nut (if I play the required number of hours). If my concerns are (in order):

Lowest ROR
Smaller bankroll swings
Profitability

Which game should I play?

[/ QUOTE ]

Utility models provide us with a notion of the "Certainty Equivalent", a risk-adjusted value of a bet. Blackjack players, who tend to be a more mathematically inclined bunch then poker players, know all about it:

http://www.bjmath.com/bjmath/kelly/kellyfaq.htm

Any rational gambler makes decisions to maximize CE or CE/hr, not EV or EV/hr.

When all possible payoffs of a gamble are small compared to your bankroll (applies to any poker game except for MTTs or jackpot games), CE=EV-Var/2R, where the second term is the cost of variance. R can be interpreted as a Kelly bankroll -- you can use R=1/3 or 1/4 bankroll. R is the single scalar parameter that describes your current risk tolerance.

Guessing that your R is on the order of $1000, I get:

Game A: CE/hr=$20/hr
Game B: CE/hr=$12/hr
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